Java實現二叉樹的前序、中序、後序、層序遍歷（非遞歸方法）

時間 2019-12-09

原文原文鏈接

在上一篇博客中，實現了Java中二叉樹的四種遍歷方式的遞歸實現，接下來，在此實現Java中非遞歸實現二叉樹的前序、中序、後序、層序遍歷，在非遞歸實現中，藉助了棧來幫助實現遍歷。前序和中序比較相似，也簡單一些，可是後序遍歷須要兩個棧來進行輔助，稍微複雜一些，層序遍歷中藉助了一個隊列來進行實現。java

一樣是那棵二叉樹函數

前序遍歷：4 2 1 3 6 5 7 8 10this
中序遍歷：1 2 3 4 5 6 7 8 10code
後序遍歷：1 3 2 5 10 8 7 6 4遞歸
層序遍歷：4 2 6 1 3 5 7 8 10隊列

import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;

public class Tree<AnyType extends Comparable<? super AnyType>>
{
    private static class BinaryNode<AnyType>
    {
        BinaryNode(AnyType theElement)
        {
            this(theElement, null, null);
        }

        BinaryNode(AnyType theElement, BinaryNode<AnyType> lt, BinaryNode<AnyType> rt)
        {
            element = theElement;
            left = lt;
            right = rt;
        }

        AnyType element;
        BinaryNode<AnyType> left;
        BinaryNode<AnyType> right;
    }

    private BinaryNode<AnyType> root;

    public void insert(AnyType x)
    {
        root = insert(x, root);
    }

    public boolean isEmpty()
    {
        return root == null;
    }

    private BinaryNode<AnyType> insert(AnyType x, BinaryNode<AnyType> t)
    {
        if(t == null)
        {
            return new BinaryNode<>(x, null, null);
        }

        int compareResult = x.compareTo(t.element);

        if(compareResult < 0)
        {
            t.left = insert(x, t.left);
        }
        else if(compareResult > 0)
        {
            t.right = insert(x, t.right);
        }
        else
        {
            ;
        }

        return t;
    }

    /**
     * 前序遍歷
     * 遞歸
     */
    public void preOrder(BinaryNode<AnyType> Node)
    {
        if (Node != null)
        {
            System.out.print(Node.element + " ");
            preOrder(Node.left);
            preOrder(Node.right);
        }
    }

    /**
     * 中序遍歷
     * 遞歸
     */
    public void midOrder(BinaryNode<AnyType> Node)
    {
        if (Node != null)
        {
            midOrder(Node.left);
            System.out.print(Node.element + " ");
            midOrder(Node.right);
        }
    }

    /**
     * 後序遍歷
     * 遞歸
     */
    public void posOrder(BinaryNode<AnyType> Node)
    {
        if (Node != null)
        {
            posOrder(Node.left);
            posOrder(Node.right);
            System.out.print(Node.element + " ");
        }
    }

    /*
     * 層序遍歷
     * 遞歸
     */
    public void levelOrder(BinaryNode<AnyType> Node) {
        if (Node == null) {
            return;
        }

        int depth = depth(Node);

        for (int i = 1; i <= depth; i++) {
            levelOrder(Node, i);
        }
    }

    private void levelOrder(BinaryNode<AnyType> Node, int level) {
        if (Node == null || level < 1) {
            return;
        }

        if (level == 1) {
            System.out.print(Node.element + "  ");
            return;
        }

        // 左子樹
        levelOrder(Node.left, level - 1);

        // 右子樹
        levelOrder(Node.right, level - 1);
    }

    public int depth(BinaryNode<AnyType> Node) {
        if (Node == null) {
            return 0;
        }

        int l = depth(Node.left);
        int r = depth(Node.right);
        if (l > r) {
            return l + 1;
        } else {
            return r + 1;
        }
    }

    /**
     * 前序遍歷
     * 非遞歸
     */
    public void preOrder1(BinaryNode<AnyType> Node)
    {
        Stack<BinaryNode> stack = new Stack<>();
        while(Node != null || !stack.empty())
        {
            while(Node != null)
            {
                System.out.print(Node.element + "   ");
                stack.push(Node);
                Node = Node.left;
            }
            if(!stack.empty())
            {
                Node = stack.pop();
                Node = Node.right;
            }
        }
    }

    /**
     * 中序遍歷
     * 非遞歸
     */
    public void midOrder1(BinaryNode<AnyType> Node)
    {
        Stack<BinaryNode> stack = new Stack<>();
        while(Node != null || !stack.empty())
        {
            while (Node != null)
            {
                stack.push(Node);
                Node = Node.left;
            }
            if(!stack.empty())
            {
                Node = stack.pop();
                System.out.print(Node.element + "   ");
                Node = Node.right;
            }
        }
    }

    /**
     * 後序遍歷
     * 非遞歸
     */
    public void posOrder1(BinaryNode<AnyType> Node)
    {
        Stack<BinaryNode> stack1 = new Stack<>();
        Stack<Integer> stack2 = new Stack<>();
        int i = 1;
        while(Node != null || !stack1.empty())
        {
            while (Node != null)
            {
                stack1.push(Node);
                stack2.push(0);
                Node = Node.left;
            }

            while(!stack1.empty() && stack2.peek() == i)
            {
                stack2.pop();
                System.out.print(stack1.pop().element + "   ");
            }

            if(!stack1.empty())
            {
                stack2.pop();
                stack2.push(1);
                Node = stack1.peek();
                Node = Node.right;
            }
        }
    }

    /*
     * 層序遍歷
     * 非遞歸
     */
    public void levelOrder1(BinaryNode<AnyType> Node) {
        if (Node == null) {
            return;
        }

        BinaryNode<AnyType> binaryNode;
        Queue<BinaryNode> queue = new LinkedList<>();
        queue.add(Node);

        while (queue.size() != 0) {
            binaryNode = queue.poll();

            System.out.print(binaryNode.element + "  ");

            if (binaryNode.left != null) {
                queue.offer(binaryNode.left);
            }
            if (binaryNode.right != null) {
                queue.offer(binaryNode.right);
            }
        }
    }

    public static void main( String[] args )
    {
        int[] input = {4, 2, 6, 1, 3, 5, 7, 8, 10};
        Tree<Integer> tree = new Tree<>();
        for(int i = 0; i < input.length; i++)
        {
            tree.insert(input[i]);
        }
        System.out.print("遞歸前序遍歷 ：");
        tree.preOrder(tree.root);
        System.out.print("\n非遞歸前序遍歷：");
        tree.preOrder1(tree.root);
        System.out.print("\n遞歸中序遍歷 ：");
        tree.midOrder(tree.root);
        System.out.print("\n非遞歸中序遍歷 ：");
        tree.midOrder1(tree.root);
        System.out.print("\n遞歸後序遍歷 ：");
        tree.posOrder(tree.root);
        System.out.print("\n非遞歸後序遍歷 ：");
        tree.posOrder1(tree.root);
        System.out.print("\n遞歸層序遍歷：");
        tree.levelOrder(tree.root);
        System.out.print("\n非遞歸層序遍歷 ：");
        tree.levelOrder1(tree.root);
    }
}

在以上代碼中，preOrder一、midOrder一、posOrder一、levelOrder1四個函數，分別表明了非遞歸實現的二叉樹前序、中序、後序、層序遍歷遍歷。element